Perpendicular lines are vertical lines that form a right angle between them, that is, an angle of 90° 90° degrees.
Perpendicular lines appear in many geometric shapes, such as a rectangle, a square, a right triangle, and others. 

Image of Perpendicular Lines

Suggested Topics to Practice in Advance

  1. Parallel lines
  2. Angles In Parallel Lines
  3. Alternate angles
  4. Corresponding angles
  5. Collateral angles
  6. Vertically Opposite Angles
  7. Adjacent angles

Practice Perpendicular Lines

Examples with solutions for Perpendicular Lines

Exercise #1

Which lines are parallel to each other?

Video Solution

Step-by-Step Solution

Let's remember that parallel lines are lines that, if extended, will never intersect.

In diagrams a'+b'+c', all the lines intersect with each other at a certain point, except for diagram d'.

The lines drawn in answer d' will never intersect.

Answer

Exercise #2

Which lines are perpendicular to each other?

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

The only drawing where it can be seen that the lines form a right angle of 90 degrees between them is drawing A.

Answer

Exercise #3

Which lines are perpendicular to each other?

Video Solution

Step-by-Step Solution

Perpendicular lines are lines that form a right angle of 90 degrees between them.

The only drawing where the lines form a right angle of 90 degrees between them is drawing A.

Answer

Exercise #4

Which figure(s) show intersecting lines?

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Video Solution

Step-by-Step Solution

Lines that intersect each other are lines that divide the side into two equal parts.

The drawings showing that the lines divide the sides into equal parts are drawings 1+3.

In drawing 2, the lines are perpendicular and vertical to each other, and in drawing 4, the lines are parallel to each other.

Answer

1 and 3

Exercise #5

Which figure shows perpendicular lines?

Video Solution

Step-by-Step Solution

Perpendicular lines are lines that form a right angle between them.

In the drawings A+C+D, you can see that the angles formed are not right angles.

It is possible to point out a right angle in drawing B.

Answer

Exercise #6

Which of the figures shows parallel lines?

Video Solution

Step-by-Step Solution

Parallel lines are lines that, if extended, will never meet.

In the drawings A+B+D if we extend the lines we will see that at a certain point they come together.

In drawing C, the lines will never meet, therefore they are parallel lines.

Answer

Exercise #7

Which of the figures show perpendicular lines?

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Video Solution

Step-by-Step Solution

Perpendicular lines are lines that form a right angle of 90 degrees between them.

It can be observed that in figures 1 and 3, the angles formed by the lines between them are right angles of 90 degrees.

Answer

1 and 3

Exercise #8

What do the four figures below have in common?

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Video Solution

Step-by-Step Solution

Let's think about the different definitions of different lines.

We can see that what all lines have in common is that they form a right angle of 90 degrees with each other.

Let's remember that lines that form a right angle of 90 degrees with each other are perpendicular and vertical lines.

Therefore, the correct answer is a.

Answer

All perpendicular

Exercise #9

What do the four figures below have in common?

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Video Solution

Step-by-Step Solution

Answer

All parallel

Exercise #10

What do the 4 figures below have in common?

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Video Solution

Step-by-Step Solution

Let's think about the different definitions of various lines.

We can see that what is common to all lines is that they intersect with each other, meaning they have a point of intersection.

We'll remember that lines that cross each other are lines that will meet at a certain point.

Therefore, the correct answer is a.

Answer

All intersections

Exercise #11

What do the four figures below have in common?

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Video Solution

Step-by-Step Solution

Let's think about the different definitions of different lines.

We can see that what all these lines have in common is that they form a right angle of 90 degrees with each other.

Let's remember that lines that form a right angle of 90 degrees with each other are perpendicular and vertical lines.

Therefore, the correct answer is a.

Answer

All perpendicular

Exercise #12

What can be said about the lines shown below?

Video Solution

Step-by-Step Solution

Let's remember the different properties of lines.

The lines are not parallel since they intersect.

The lines are not perpendicular since they do not form a right angle of 90 degrees between them.

Therefore, no answer is correct.

Answer

None of the above.

Exercise #13

Which lines are perpendicular to each other?

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form an angle of 90 degrees between them.

In each of the answers, we will draw the letter T at the point of intersection of the lines.

Let's examine figure A:

We notice that the lines do form a right angle and the lines are perpendicular to each other.

Let's examine figure B:

We notice that the lines do not meet and do not form any angle; therefore, they are parallel lines and not perpendicular.

Answer

Exercise #14

Which of the lines are perpendicular to each other?

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines are lines that form a right angle of 90 degrees between them.

In each of the answers, we will draw the letter T at the point of intersection of the lines.

Let's examine figure A:

We will notice that the lines do not form a right angle, and therefore are not perpendicular.

Let's examine figure B:

The lines do indeed form a 90-degree angle and are therefore perpendicular.

Let's examine figure C:

We notice that the lines do not form a right angle, and therefore are not perpendicular.

Answer

Exercise #15

Which of these lines are perpendicular to each other?

Video Solution

Step-by-Step Solution

Let's remember that perpendicular lines form a 90-degree angle.

In each of the answers, we will draw the letter T at the intersection point of the lines.

Let's examine figure A:

We notice that the lines do not form a right angle and therefore are not perpendicular.

Let's examine figure B:

We notice that the lines do not form a right angle and therefore are not perpendicular.

Let's examine figure C:

We notice that the lines do not form a right angle and therefore are not perpendicular.

Let's examine figure D:

We notice that the lines do form a right angle therefore are perpendicular lines.

Answer